I am a permanent resident living in Canada; I hold a British passport. I am travelling back to the UK for a holiday, and was wondering whether, when arriving, am I able to walk straight through or do I have to join the line up as if I were a visitor?
As you're a British citizen, you'll be allowed into the UK with minimal fuss whether or not you actually live there. The border guards won't know or care what country you're living in, and are very unlikely to ask you any questions at all.
When you arrive in the UK, join the "UK and EU passports" line at passport control. You'll still have to wait (possibly a while at larger airports) but this line usually moves much faster than the line for non-EU folks.
EDIT: Notts90 raises a good point about which country you mean by "home". If you're talking about returning to Canada as a permanent resident, you'll still have to wait at passport control, although there might be a separate line for permanent residents.
As a citizen of the UK, you are entitled to enter the UK. To get past the immigration checkpoint, however, you have to establish to the satisfaction of an immigration officer that you are a citizen of the UK. That means that you must wait for an available immigration officer (or automated passport gate) if one is not immediately available. Furthermore, you have to stop at the gate or at the officer's desk to show your passport and wait for any validation process to be completed.
This process is much quicker than the full immigration checks that non-EU/EEA/Swiss travelers go through, so the line you will join will generally be much shorter and faster moving, but you certainly can't characterize it as "walking straight through."